Python numpy.compat.integer_types() Examples

The following are code examples for showing how to use numpy.compat.integer_types(). They are from open source Python projects. You can vote up the examples you like or vote down the ones you don't like.

Example 1
Project: LaserTOF   Author: kyleuckert   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 2
Project: LaserTOF   Author: kyleuckert   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 3
Project: LaserTOF   Author: kyleuckert   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 4
Project: LaserTOF   Author: kyleuckert   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 5
Project: FX-RER-Value-Extraction   Author: tsKenneth   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 6
Project: FX-RER-Value-Extraction   Author: tsKenneth   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2., ..., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 7
Project: FX-RER-Value-Extraction   Author: tsKenneth   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 8
Project: FX-RER-Value-Extraction   Author: tsKenneth   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 9
Project: FX-RER-Value-Extraction   Author: tsKenneth   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20., ..., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 10
Project: recruit   Author: Frank-qlu   File: test_helper.py    Apache License 2.0 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 11
Project: recruit   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 12
Project: recruit   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 13
Project: recruit   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 14
Project: recruit   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 15
Project: att   Author: Centre-Alt-Rendiment-Esportiu   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 16
Project: att   Author: Centre-Alt-Rendiment-Esportiu   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 17
Project: att   Author: Centre-Alt-Rendiment-Esportiu   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 18
Project: att   Author: Centre-Alt-Rendiment-Esportiu   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 19
Project: FUTU_Stop_Loss   Author: BigtoC   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 20
Project: FUTU_Stop_Loss   Author: BigtoC   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 21
Project: FUTU_Stop_Loss   Author: BigtoC   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 22
Project: FUTU_Stop_Loss   Author: BigtoC   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 23
Project: FUTU_Stop_Loss   Author: BigtoC   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 24
Project: MARRtino-2.0   Author: DaniAffCH   File: test_helper.py    GNU General Public License v3.0 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 25
Project: MARRtino-2.0   Author: DaniAffCH   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2., ..., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 26
Project: MARRtino-2.0   Author: DaniAffCH   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 27
Project: MARRtino-2.0   Author: DaniAffCH   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 28
Project: MARRtino-2.0   Author: DaniAffCH   File: helper.py    GNU General Public License v3.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20., ..., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 29
Project: auto-alt-text-lambda-api   Author: abhisuri97   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 30
Project: auto-alt-text-lambda-api   Author: abhisuri97   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 31
Project: auto-alt-text-lambda-api   Author: abhisuri97   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 32
Project: auto-alt-text-lambda-api   Author: abhisuri97   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 33
Project: vnpy_crypto   Author: birforce   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = tmp.ndim
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 34
Project: vnpy_crypto   Author: birforce   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = tmp.ndim
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 35
Project: vnpy_crypto   Author: birforce   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 36
Project: vnpy_crypto   Author: birforce   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 37
Project: ble5-nrf52-mac   Author: tomasero   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 38
Project: ble5-nrf52-mac   Author: tomasero   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 39
Project: ble5-nrf52-mac   Author: tomasero   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 40
Project: ble5-nrf52-mac   Author: tomasero   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 41
Project: ble5-nrf52-mac   Author: tomasero   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 42
Project: Computable   Author: ktraunmueller   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 43
Project: Computable   Author: ktraunmueller   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of fftshift.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 44
Project: Computable   Author: ktraunmueller   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 45
Project: Computable   Author: ktraunmueller   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 46
Project: poker   Author: surgebiswas   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 47
Project: poker   Author: surgebiswas   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 48
Project: poker   Author: surgebiswas   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 49
Project: poker   Author: surgebiswas   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 50
Project: P3_image_processing   Author: latedude2   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 51
Project: P3_image_processing   Author: latedude2   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2., ..., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 52
Project: P3_image_processing   Author: latedude2   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 53
Project: P3_image_processing   Author: latedude2   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 54
Project: P3_image_processing   Author: latedude2   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20., ..., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 55
Project: GraphicDesignPatternByPython   Author: Relph1119   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 56
Project: GraphicDesignPatternByPython   Author: Relph1119   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 57
Project: GraphicDesignPatternByPython   Author: Relph1119   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 58
Project: GraphicDesignPatternByPython   Author: Relph1119   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 59
Project: GraphicDesignPatternByPython   Author: Relph1119   File: helper.py    MIT License 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 60
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 61
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = n-(n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 62
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 63
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 64
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    tmp = asarray(x)
    ndim = len(tmp.shape)
    if axes is None:
        axes = list(range(ndim))
    elif isinstance(axes, integer_types):
        axes = (axes,)
    y = tmp
    for k in axes:
        n = tmp.shape[k]
        p2 = (n+1)//2
        mylist = concatenate((arange(p2, n), arange(p2)))
        y = take(y, mylist, k)
    return y 
Example 65
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) 
Example 66
Project: 3dprinteros-client   Author: panasevychol   File: helper.py    GNU Affero General Public License v3.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 67
Project: predictive-maintenance-using-machine-learning   Author: awslabs   File: test_helper.py    Apache License 2.0 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 68
Project: predictive-maintenance-using-machine-learning   Author: awslabs   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 69
Project: predictive-maintenance-using-machine-learning   Author: awslabs   File: helper.py    Apache License 2.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 70
Project: predictive-maintenance-using-machine-learning   Author: awslabs   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 71
Project: predictive-maintenance-using-machine-learning   Author: awslabs   File: helper.py    Apache License 2.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 72
Project: fund   Author: Frank-qlu   File: test_helper.py    Apache License 2.0 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 73
Project: fund   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 74
Project: fund   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 75
Project: fund   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val 
Example 76
Project: fund   Author: Frank-qlu   File: helper.py    Apache License 2.0 4 votes vote down vote up
def rfftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies
    (for usage with rfft, irfft).

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,     n/2-1,     n/2] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n)   if n is odd

    Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
    the Nyquist frequency component is considered to be positive.

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = np.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = np.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
    >>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0/(n*d)
    N = n//2 + 1
    results = arange(0, N, dtype=int)
    return results * val 
Example 77
Project: pySINDy   Author: luckystarufo   File: test_helper.py    MIT License 4 votes vote down vote up
def test_equal_to_original(self):
        """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
        from numpy.compat import integer_types
        from numpy.core import asarray, concatenate, arange, take

        def original_fftshift(x, axes=None):
            """ How fftshift was implemented in v1.14"""
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        def original_ifftshift(x, axes=None):
            """ How ifftshift was implemented in v1.14 """
            tmp = asarray(x)
            ndim = tmp.ndim
            if axes is None:
                axes = list(range(ndim))
            elif isinstance(axes, integer_types):
                axes = (axes,)
            y = tmp
            for k in axes:
                n = tmp.shape[k]
                p2 = n - (n + 1) // 2
                mylist = concatenate((arange(p2, n), arange(p2)))
                y = take(y, mylist, k)
            return y

        # create possible 2d array combinations and try all possible keywords
        # compare output to original functions
        for i in range(16):
            for j in range(16):
                for axes_keyword in [0, 1, None, (0,), (0, 1)]:
                    inp = np.random.rand(i, j)

                    assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
                                              original_fftshift(inp, axes_keyword))

                    assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
                                              original_ifftshift(inp, axes_keyword)) 
Example 78
Project: pySINDy   Author: luckystarufo   File: helper.py    MIT License 4 votes vote down vote up
def fftshift(x, axes=None):
    """
    Shift the zero-frequency component to the center of the spectrum.

    This function swaps half-spaces for all axes listed (defaults to all).
    Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to shift.  Default is None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    ifftshift : The inverse of `fftshift`.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
    >>> np.fft.fftshift(freqs)
    array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])

    Shift the zero-frequency component only along the second axis:

    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.fftshift(freqs, axes=(1,))
    array([[ 2.,  0.,  1.],
           [-4.,  3.,  4.],
           [-1., -3., -2.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [dim // 2 for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = x.shape[axes] // 2
    else:
        shift = [x.shape[ax] // 2 for ax in axes]

    return roll(x, shift, axes) 
Example 79
Project: pySINDy   Author: luckystarufo   File: helper.py    MIT License 4 votes vote down vote up
def ifftshift(x, axes=None):
    """
    The inverse of `fftshift`. Although identical for even-length `x`, the
    functions differ by one sample for odd-length `x`.

    Parameters
    ----------
    x : array_like
        Input array.
    axes : int or shape tuple, optional
        Axes over which to calculate.  Defaults to None, which shifts all axes.

    Returns
    -------
    y : ndarray
        The shifted array.

    See Also
    --------
    fftshift : Shift zero-frequency component to the center of the spectrum.

    Examples
    --------
    >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
    >>> freqs
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])
    >>> np.fft.ifftshift(np.fft.fftshift(freqs))
    array([[ 0.,  1.,  2.],
           [ 3.,  4., -4.],
           [-3., -2., -1.]])

    """
    x = asarray(x)
    if axes is None:
        axes = tuple(range(x.ndim))
        shift = [-(dim // 2) for dim in x.shape]
    elif isinstance(axes, integer_types):
        shift = -(x.shape[axes] // 2)
    else:
        shift = [-(x.shape[ax] // 2) for ax in axes]

    return roll(x, shift, axes) 
Example 80
Project: pySINDy   Author: luckystarufo   File: helper.py    MIT License 4 votes vote down vote up
def fftfreq(n, d=1.0):
    """
    Return the Discrete Fourier Transform sample frequencies.

    The returned float array `f` contains the frequency bin centers in cycles
    per unit of the sample spacing (with zero at the start).  For instance, if
    the sample spacing is in seconds, then the frequency unit is cycles/second.

    Given a window length `n` and a sample spacing `d`::

      f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
      f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd

    Parameters
    ----------
    n : int
        Window length.
    d : scalar, optional
        Sample spacing (inverse of the sampling rate). Defaults to 1.

    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = np.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = np.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

    """
    if not isinstance(n, integer_types):
        raise ValueError("n should be an integer")
    val = 1.0 / (n * d)
    results = empty(n, int)
    N = (n-1)//2 + 1
    p1 = arange(0, N, dtype=int)
    results[:N] = p1
    p2 = arange(-(n//2), 0, dtype=int)
    results[N:] = p2
    return results * val
    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d)